We know the derivative of lnx, which is ¹⁄ₓ.
(lnx)' = ¹⁄ₓ
We can find the derivative of ln(√x) using one of the following two methods.
Method 1 (Using Chain Rule) :
If y = ln(√x), find ᵈʸ⁄dₓ.
Let t = √x.
Then, we have
y = lnt
By chain rule,
Substitute y = lnt and t = √x.
Substitute t = √x.
Therefore,
Method 2 (Without Chain Rule) :
If y = ln(√x), find ᵈʸ⁄dₓ.
Use the Power Rule of Logarithms.
Find the derivative on both sides with respect to x.
Therefore,
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